Numerical and Experimental Study of Heat Pipes Used in Solar Applications

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in Solar Applications

Kods Grissa

To cite this version:

Kods Grissa. Numerical and Experimental Study of Heat Pipes Used in Solar Applications. Other. ISAE-ENSMA Ecole Nationale Supérieure de Mécanique et d’Aérotechique - Poitiers, 2018. English. �NNT : 2018ESMA0012�. �tel-02006392�

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THÈSE

Pour l’obtention du Grade de

DOCTEUR DE L’ÉCOLE NATIONALE SUPÉRIEURE

DE MÉCANIQUE ET D’AÉROTECHNIQUE

en partenariat international avec

L’ECOLE NATIONALE D'INGENIEURS DE MONASTIR

(Diplôme National – Arrêté du 25 mai 2016) École Doctorale :

SCIENCES ET INGENIERIE EN MATERIAUX, MECANIQUE, ENERGETIQUE ET AERONAUTIQUE

Secteur de Recherche : Énergétique, thermique et combustion

Présentée par :

Kods GRISSA

Numerical and experimental study of heat pipes used in

solar applications

Directeurs de thèse : Yves BERTIN et Abdelmajid JEMNI Co-Encadrant : Adel M. BENSELAMA

****************************

Soutenue le mardi 18 Décembre 2018 devant la Commission d’Examen

****************************

JURY

Rapporteurs :

M. Abdulmajeed A. MOHAMAD, Professeur, Université de Calgary, Canada

M. Mohamed Chaker ZAGHDOUDI, Professeur à l’INSAT, Université de Carthage, Tunisie

Membres du jury :

Mme. Souad HARMAND, Professeur à l'Université de Valenciennes et du Hainaut-Cambrésis, France M. Ezeddine SEDIKI, Professeur à la FST, Université Tunis El Manar, Tunisie

M. Abdelmajid JEMNI, Professeur à l’ENIM, Université de Monastir, Tunisie M. Yves BERTIN, Professeur à l’ISAE-ENSMA, France

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Firstly, I would like to thank God for immensely blessing and providing me with eve-rything needed to achieve all that I have accomplished. I am grateful to work in two highly qualiﬁed laboratory of research ( Laboratoire d’Etude des Systémes thermiques et Energétique (LESTE) and Institut Pprime). Under the direction of Pr. Abdelmajid Jemni and Pr. Yves Bertin, I have learned much through their experience. A special thanks goes to my supervisor Dr. Adel M. Benselama for invaluable assistance, guidance and support during my thesis at Institut Pprime. He was my source of encouragement and motivation especially in the bad moments. Through your exemplary working method and technical knowledge, he has been always a source of inspiration.

I would like to express my special thanks to Dr. Raoudha Chaabane and Dr. Zied Lataoui for their precious comments on my work, their motivation and support during my thesis in LESTE. Another sincere acknowledgement is for Dr. Cyril Romestant, a research en-gineer at the Prime Institut. His guidance, support and previous experiences in thermal engineering were a constant source of reliable knowledge. Also, he allowed for the experi-mental portion of this thesis to be relative. Special thanks goes to Dr. Vincent Ayel and Dr. Nicolas Chauris for their time and support. A special thanks goes to Mr. Hérvé Arlaub and Mr. André Piteau for their continuous help and assistance during the experimental setup. Without their knowledge and skills the experimental setup would have been more time consuming and less successful then it was.

I would like to thank all the COST members especially Fillipo for his help supporting me while doing my experiments. Also, I would like to thank all the LESTE members especially Abir Yahia. Their tireless eﬀorts are sincerely appreciated. Working for both teams has been a privilege and a pleasure throughout the years.

Profuse thanks go equally to Pr. Abdulmajeed Mohamad and Pr. Mohamed Zaghdoudi for accepting reporting my thesis. Also, I would like to thank Pr. Souad Harmand and Pr. Ezeddine Sediki for being part of the jury board of my PhD.

Last but not least I would like to thank Eiﬀel Scholarship, which made this PhD thesis possible through their ﬁnancial support under the following number 870763D.

I would like to thank my parents, Mohamed and Emna, for their encouragement and sup-port for me during my challenges. I would also like to thank my sisters Najla and Hajer and my brothers Saif, Tarek and Zied for their words of encouragement and understanding during my studies.

Most importantly, I would like to thank my husband Abdou for his perfect grace and sacriﬁce, for giving me the talent, resources and strength to continue for my accomplish-ments. I praise him for the joy he gives me and the passion he has given me for life. Finally, I dedicate this thesis to my future baby.

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List of figures

1 Energy consumption of heating networks in million tonnes of oil equivalent

(mtoe) by source [152]. . . 2

2 The primary production of renewable energies in mtoe by sector in 2015 [152]. 3 3 The residential energy consumption in mtoe per type of energy in France [152]. 3 4 The rate of installed surface in m2 _{per year for each solar collector} techno-logy [152]. . . 4

5 The installed surface in m2 _{per year for each collector technology [}₁₅₂_]. _{. .} ₄

1.1 Drawing of Perkin’s boiler [229]. . . 8

1.2 Heat pipe schematic description.. . . 10

1.3 Diﬀerent wick structures used in heat pipes [229]. . . 14

1.4 Thermosyphon. . . 20

1.5 Schematics of a pulsating heat pipe [229].. . . 21

1.6 Schematics of loop heat pipes [229]. . . 22

1.7 Heat pipe limits [229]. . . 24

1.8 One tube HPETSC schematic description. . . 32

1.9 Heat pipe evacuated tube solar collector. . . 32

1.10 HPETSC with bad contact between the ﬁnner and the inner tube [1]. . . . 37

1.11 Cross section of the evacuated tube heat pipe in case of inserting (a) ﬁnned surface (b) ﬁnned surface and oil and (c) foamed copper and oil. Courtesy of [1] (adapted). . . 38

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1.12 Heat transfer process in LHTES tank. (a) solar heat absorption, (b) PCM charging and (c) PCM discharging and water supply heating. Courtesy

of [192] (adapted). . . 38

1.13 Schematic of HPETSC ﬁlled with PCM. Courtesy of [208] (adapted). . . . 39

1.14 HPSC-LHS system [193] (adapted). . . 40

1.15 Solar intensity for a black body at 5800K and a heat pipe at 310K. . . 40

1.16 Aluminum ﬁnned HP proposed by the authors: (a) outer view of the HP’s fragment and (b) cross-sectional proﬁle of the HP: 1-absorber and 2-grooved HP. [228]. . . 43

1.17 Photography of manifold header prototype from diﬀerent phase of manu-facturing (A)-illustration of inner arrangement, (B)-front view of partially assembled manifold, (C)-comparison of standard manifold (top) and pro-totype of manifold header (bottom), where is clearly visible similar dimen-sions [242]. . . 44

2.1 Scheme of D2Q9 lattice. . . 54

2.2 Boundary distribution functions [186]. . . 58

2.3 Half way bounce back. . . 59

2.4 Symmetry boundary condition. . . 62

2.5 Scheme of the implimented boundary condition. . . 63

2.6 Periodic boundary condition [186]. . . 65

2.7 D1Q5 lattice. . . 67

2.8 D2Q9 lattice (recall of ﬁgure 2.1). . . 68

2.9 D3Q19 lattice. . . 69

2.10 LBM algorithm synoptic. . . 72

2.11 pre-streaming step (a) and post-streaming step (b). Note the propagation of the information. . . 75

3.1 Symmetry axis boundary; dashed-dotted line: symmetry axis; and dashed line: ghost boundary along symmetry axis. . . 86

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the ﬁrst test as obtained from the present LBE model simulation (solid lines) versus the closed-form solution (symbols) for the ﬁrst test case. . . . 93

3.4 A comparison of the axial velocity proﬁles for diﬀerent permeabilities as ob-tained from the present LBE model simulation (solid lines) and the

closed-form solution (symbols) for the second test case with Forchheimer term. . . 95

3.5 A comparison of the axial velocity proﬁles for diﬀerent permeabilities as obtained from the present LBE model simulation (solid lines) and the

nu-merical solution by Rong et al. [238] (symbols) for the second test case

without Forchheimer term. . . 95

3.6 Illustration of the third case test. . . 96

3.7 A comparison of the axial velocity proﬁles for diﬀerent permeability as obtained from the present LBE model simulation (solid lines) without

For-chheimer term versus the closed-form solution (symbols) for the third test. 97

3.8 A comparison of the axial velocity proﬁles for diﬀerent permeability of the third test case as obtained from the present LBE model simulation (solid lines) with Forchheimer term versus numerical solution by Rong et al. [238] (symbols). . . 97

3.9 Schematic diagram of the fourth case test. . . 98

3.10 A comparison of the 3.10a axial velocity and 3.10b temperature proﬁles of the fourth test case as obtained from the present LBE model simulation (solid lines) versus the results of Rong et al. [241] (symbols). . . 99

3.11 L2-norm errors with respect to mesh resolution for the diﬀerent test case for

the proposed LBE model (⊲ symbols) and its enhanced version (◦ symbols).106

4.1 Heat pipe schematic description. (Lengths are not to scale.) . . . 108

4.2 Half lattice division for the solid/ﬂuid interface processing; dashed line: solid/ﬂuid interface; A: one lattice on the liquid; B: one lattice on the solid.111

4.3 Artificial seperation of the domain into two parts at the solid/fluid inter-face; solid red line: solid/fluid interface. . . 111

4.4 Vapor-liquid interface. . . 112

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4.6 Comparison between velocity proﬁles obtained from the present LBE model simulation (solid line) and from the results of Brahim et al. (symbols) [20]. (a) the axial velocity along the vapor core center, (b) the radial velocity

along the liquid-vapor interface. . . 115

4.7 A comparison of the present LBE model simulation (solid line) with the analytical results of Zhu et al. [319] (⊲ symbols) and the experimental results of Huang et al. [159] (◦ symbols). . . 118

4.8 L2-norm errors versus the grid spacing. . . 118

4.9 Resistance circuit equivalent to the heat pipe. . . 120

4.10 Profiles for different working fluid. . . 123

4.11 Proﬁles in the liquid/wick region for diﬀerent wick structures. . . 125

4.12 Heat pipe coupled to heat exchanger. (All sizes are given in mm.) . . . 126

4.13 Variations of thermal resistance versus heat input density for diﬀerent wor-king ﬂuids. . . 128

4.14 Variations of thermal resistance versus the porosity for diﬀerent working ﬂuids and permeability equal to 1.17 × 10−11_m−2_. _{. . . 129}

4.15 Variations of thermal resistance versus the permeability for diﬀerent wor-king ﬂuids and porosity set to 0.4. . . . 129

4.16 Variations of thermal resistance versus the wick thickness for diﬀerent wor-king ﬂuids. . . 131

4.17 Variations of the ratio of thermal resistance versus the evaporator length for diﬀerent working ﬂuids. . . 132

4.18 Variations of thermal resistance versus the sine of inclination angle for diﬀerent working ﬂuids. . . 133

4.19 Cross section of heat pipe evacuated tube solar collector. . . 134

4.20 General description of heat pipe evacuated tube solar collector. . . 135

4.21 Heat pipe evacuated tube solar collector. . . 135

4.22 The evolution of (4.22a) outlet temperature, (4.22b) energy efficiency and (4.22c) exergy efficiency for different solar radiations. . . 139

4.23 The evolution of (4.23a) outlet temperature, (4.23b) energy efficiency and (4.23c) exergy efficiency for different tubes numbers.. . . 140

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5.2 Condenser bundles. . . 145

5.3 Evaporator block. . . 146

5.4 Thermocouple implementation. . . 147

5.5 Details of thermocouple locations in test bench in cm.. . . 148

5.6 Leak test. . . 148

5.7 Temperature measurement technique. . . 150

5.8 Calibration bench test. . . 151

5.9 Ertalon support. . . 151

5.10 Isolated heat pipe. . . 152

5.11 Filling system.. . . 156

5.12 Schematic of case A. . . 157

5.13 Schematic of case B. . . 158

5.14 Schematic of case C. . . 158

5.15 The distributions of the 18 points given in table 5.5 and represented by a circle. . . 160

5.16 Generated points using the LHS for water. . . 161

5.17 Comparison between the LHS and the experimental results. . . 162

5.18 Resistance circuit equivalent to the heat pipe. . . 163

5.19 Illustration of solar incident radiation. . . 163

5.20 Schematic of the symmetric and asymmetric heating conﬁgurations. . . 164

5.21 Variations of the thermal resistance versus the heat input for different fluids and filling ratios using symmetric and asymmetric configurations under condenser temperature, 37◦_{C, and inclination angle, 63}◦_. _{. . . 165}

5.22 Variations of the thermal resistance versus the heat input for diﬀerent ﬁlling ratios under condenser temperature, 37◦_{C, and inclination angle, 63}◦_. _{. . . 167}

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5.23 Variations of the thermal resistance versus the heat input for diﬀerent wor-king ﬂuids under condenser temperature, 37◦_{C, and inclination angle, 63}◦_. ₁₆₈

5.24 Variations of the thermal resistance versus heat input density for diﬀerent working ﬂuids for a HP with 1.76m of length (1.4m evaporator, 0.06m adia-batic and 0.3 condenser length), ε = 0.4, K = 1.17 × 10−10_m−2_{, convective}

heat transfer coeﬃcient of 1400W.m−2_.K−1 _{and inlet temperature of 22}◦_C. ₁₆₈

5.25 Gravity-assisted and gravity-opposed orientations. . . 169

5.26 Variations of the thermal resistance versus the inclination angle under

condenser temperature, 55◦_{C, and heat input, 47.75W.} _{. . . 170}

5.27 Variations of thermal resistance versus the sine of inclination angle for dif-ferent working ﬂuids for a HP with 1.76m of length (1.4m evaporator, 0.06m adiabatic and 0.3 condenser length), ε = 0.4, K = 1.17×10−10_m−2_,

convec-tive heat transfer coeﬃcient of 1400W.m−2_.K−1 _{and inlet temperature of}

22◦_C. _{. . . 171}

5.28 Variations of the thermal resistance versus the condenser temperature un-der inclination angle, 63◦_{, and heat input, 38.75W.} _{. . . 172}

5.29 Variations of the wall temperature versus the heat pipe length using wa-ter as working ﬂuid by referring to experimental and numerical results for gravity-assisted and gravity-opposed orientations under condenser tempe-rature, 10◦_{C, and heat input, 5W.} _{. . . 173}

5.30 Variations of the wall temperature versus the heat pipe length using me-thanol as working ﬂuid by referring to experimental and numerical results for gravity-assisted and gravity-opposed orientations under condenser tem-perature, 10◦_{C, and heat input, 5W.} _{. . . 174}

5.31 Variations of the maximum heat input versus the operation temperature for (5.31a) water and (5.31b) methanol.. . . 175

5.32 Temperature iso-contours in ◦_{C in the wall/liquid-wick region using water}

as working ﬂuid by referring to numerical results for gravity-assisted and

gravity-opposed orientations under condenser temperature, 10◦_{C, and heat}

input, 5W. . . 176

5.33 Temperature iso-contours in◦_{C in the wall/liquid-wick region using}

metha-nol as working ﬂuid by referring to numerical results for gravity-assisted

and gravity-opposed orientations under condenser temperature, 10◦_{C, and}

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king ﬂuid by referring to numerical results for assisted and

gravity-opposed orientations under condenser temperature, 10◦_{C, and heat input,}

5W. . . 177

5.35 Axial liquid-wick velocity iso-contours in ×10−1_{m/s using methanol as}

wor-king ﬂuid by referring to numerical results for assisted and

gravity-opposed orientations under condenser temperature, 10◦_{C, and heat input,}

5W. . . 178

5.36 Axial vapor velocity iso-contours in m/s using water as working ﬂuid by re-ferring to numerical results for gravity-assisted and gravity-opposed

orien-tations under condenser temperature, 10◦_{C, and heat input, 5W.} _{. . . 179}

5.37 Axial vapor velocity iso-contours in m/s using methanol as working ﬂuid by referring to numerical results for gravity-assisted and gravity-opposed

orientations under condenser temperature, 10◦_{C, and heat input, 5W.} _{. . . 179}

5.38 A comparison of the error between the experimental and numerical results for the tested points (1 to 5 given in table 5.5) by varying the condenser

temperature, the inclination angle and the heat input power. . . 181

5.39 Variations of the thermal resistance versus the heat input for different fluids and filling ratios configurations with and without the adiabatic region under condenser temperature, 37◦_{C, and inclination angle, 63}◦_. _{. . . 182}

5.40 Variations of the thermal resistance versus the heat input for water with 150% ﬁlling ratios using symmetric and asymmetric conﬁgurations under condenser temperature, 37◦_{C, and inclination angle, 63}◦_. _{. . . 183}

5.41 The optimum heat input versus the inclination angle. . . 186

B.1 Temperature ﬁeld in the porous medium expressed in◦_{C for diﬀerent}

wor-king ﬂuids using sintered steel (case I). . . 198

wor-king ﬂuids using copper screen (case II). . . 198

wor-king ﬂuids using sintered copper (case III). . . 199

B.4 Axial velocity field expressed in the vapor core in m/s for different working fluids using sintered steel in the vapor region (case I). . . 199

B.5 Axial velocity field expressed in the vapor core in m/s for different working fluids using copper screen in the vapor region (case II). . . 200

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B.6 Axial velocity ﬁeld expressed in the vapor core in m/s for diﬀerent working

ﬂuids using sintered copper in the vapor region (case III). . . 200

C.1 Heat pipe sizes. . . 201

D.1 Evaporator design ﬁrst version. . . 204

D.2 Evaporator design second version. . . 205

D.3 Condenser design ﬁrst version. . . 206

D.4 Condenser design ﬁrst second version. . . 207

D.5 Bench test. . . 208

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List of tables

1.1 Heat pipe main working ﬂuids [229].. . . 12

1.2 Working ﬂuids and their compatibility with heat pipe wick material. . . 13

1.3 Classiﬁcation of heat transfer ﬂuids temperature range [237]. . . 25

4.1 Heat pipe validation parameters [20]. . . 116

4.2 Heat pipe validation parameters [319]. . . 117

4.3 Thermophysical properties of the working ﬂuids at standard conditions. . . 120

4.4 Heat pipe parameters. . . 122

4.5 Thermal resistance, Rth, for diﬀerent working ﬂuids. . . 122

4.6 Proprieties of the diﬀerent wick structure. . . 124

4.7 Thermal resistance, Rth, for diﬀerent wick structure. . . 124

4.8 Heat pipe parameters. . . 126

4.9 Thermal resistance (Rth(K.W−1_{)) of each case for different working fluids} and different wick structures. . . 130

4.10 HPETSC parameters.. . . 138

5.1 Heat pipe characteristics parameters. . . 144

5.2 Uncertainty of temperature measurement. . . 154

5.3 Heat pipe functionality limits for water at 35◦_C. _{. . . 158}

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5.5 The experimental measurement points. . . 160

5.6 Comparison between the numerical and experimental resistances for

dif-ferent experimental tested points using water as working ﬂuid. . . 180

5.7 Comparison between the numerical and experimental resistances for

dif-ferent experimental tested points using methanol as working ﬂuid. . . 180

F.1 Thermal resistance at 30◦_{C under heat input of 5W for case A.}_{. . . 213}

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Nomenclature

Greek letters

α Thermal diffusion coefficient (m2_._s−1₎ β Thermal expansion coefficient (K−1)

∆t Time step (s)

∆x Space step in the x direction (m)

δi,j Kronecker symbol

γ Ratio of the vapor speciﬁc heat capacity (cp/cv)

λ Thermal conductivity (W.m−1_._K−1₎

(τα)_e Collector eﬀective transmittance-absorptance product

µ Dynamic viscosity (kg.m−1_._s−1₎ ν Kinetic viscosity (m2_._s−1₎

Ω Collision operator

ρ Density (kg.m−3₎

σ liquid-vapor surface tension (N.m−1₎

σ′ Ratio between the heat capacities of the porous medium solid and liquid phases τ Relaxation time (s)

Θ Forcing term in the mass equation

θ Tilt angle (◦₎

ε Porosity of the porous medium

e

σ Accommodation coeﬃcient Latin letters

˙m Mass ﬂow rate (kg.s−1₎

a Acceleration (m.s−2₎

c Lattice velocity vector G Body force (N)

g Gravitational acceleration (m.s−2₎

I Identity matrix

u Velocity vector (m.s−1₎

x Position (m)

Ac Collector aperture area (m2)

cs Speed of sound

cp Thermal capacity at constant pressure (J.kg−1.K−1)

cv Thermal capacity at constant volume (J.kg−1.K−1)

D Dimension of the problem dp Pores mean diameter (m)

f Velocity distribution function F′ Removal factor

Fα Forcing term in the momentum equation

Fε Geometric function

Fp Source term due to the presence of porous medium

g Temperature distribution function hlv Latent heat of vaporization (J.kg−1)

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I Solar radiation intensity (W.m−2₎ i Position in the z-direction

j Position in the r-direction K Permeability (m−2₎

L Length (m)

M Molar mass (g.mol−1₎

m Number of cells in the r-direction

Me Merit number

n Number of cells in the z-direction

p Pressure (Pa) Q Heat input (W)

q Heat ﬂux density (W.m−2₎ R Dimensionless radial coordinate r Radial coordinate (m)

Rg Ideal gas constant (8.314 J.mol−1K−1)

S Surface (m2₎ T Temperature (K) t Time (s)

u Axial velocity (m.s−1₎

UL Heat loss coeﬃcient (W.m−2.K−1)

V Volume (m3₎

v Radial velocity (m.s−1₎

w Weight

Z Dimensionless axial coordinate z Axial coordinate (m) Dimensionless numbers Bi Biot number(= H R/λ) Da Darcy number (= K/L2₎ Ma Mach number (= V/c0) Pr Prandtl number(= ν/α) Ra _{Rayleigh number (= gβ(T − T}0)R3/να) Re Reynolds number (= U R/ν) Superscripts ′ _{Symmetry component} eq Equilibrium neq Non-equilibrium Subscripts 0 Reference adia Adiabatic b Boiling cond Condenser crit Critical e Eﬀective ent Entertainment envi Environmental evap Evaporator f Fluid g Gas g Meniscus in Inlet k Lattice direction l Liquid

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out Outlet p Porous wick

phy Physical units P T Contact line r Radial s Solid sat Saturation sol Solar son Sonic tot Total v Vapor vis Viscous w Wall z Axial

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1 Context

As in the last century the world’s population quadrupled, from two to eight billion people, and its corollary the world’s economy growing, the demand for energy is also seve-rely increasing at a substantial rate. Currently, this high energy demand mainly depends on non-renewable energy sources such as oil, gas and fossil fuel resources. As some of these energy sources previously mentioned have reached, or are close to reaching, their peak sup-ply, we are expected toward a major energy crisis if no applicable substitutions are found. Besides, the difficulty of meeting the high energy demand, the issue of environment and sustainability has led to a critical concern on power generation and utilization. Fossil fuels are sources of emissions which contribute to the global warming and are unsustainable due to their dwindling reserves, price rise and geographic origin not evenly distributed in the world. Geopolitical instability in resource areas is also a major concern. Due to this energy and environmental issues of non-renewable sources, more attention is being given to renewable energy sources which are environmentally friendly and sustainable. Renewable energy sources such as solar energy are the long term options to substitute conventional energies. It reduces electric/auxiliary energy usage with free solar energy and COX, NOX, SOX emissions. Recently, France used significantly less fossil resources and significantly more renewable power (see figure1). There was also a decline in natural gas for domestic heat use, which remains the main source, and increases in renewable power, which represents the third primary energy consumption, according to “Key figures of energy, 2016 Edition”.

Figure 1 – Energy consumption of heating networks in million tonnes of oil equivalent (mtoe) by source [152].

In the recent years solar energy has been strongly promoted as a reliable energy source. One of the most straight forward applications of this energy is converting solar radiation into heat, for example in hot water supply. In 2015, we can see, in ﬁgure 2, the primary

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production of renewable energies amounted to 23Mtoe in a typical french city where the thermal solar and photovoltaic contribution is about 0.7% only the scope for progress is tremendous.

Figure2 – The primary production of renewable energies in mtoe by sector in 2015 [152]. However, the solar water heating technology has greatly improved during the past three decades. Today there are more than 30 million square meters of solar collectors installed around the planet. These technologies are usually at either the industrial or residential scale. At the residential scale, home owners can produce their own hot water from the sun to offset the fluctuations and inflation of gas and electric energy costs. A residential solar water heating system normally consists of the solar collector, the tank used to store the generated hot water, and other components that might be used for auxiliary energy or automated control. In 2015, the energy consumption in the residential-commercial sector amounted to 67.0Mtoe. Compared to 2014, this value is increased by 0.3% (see figure 3). Since 1980, the consumption of petroleum products has declined steadily in favor of gas and electricity. While, for renewable energies, their consumption has increased every year by 4% on average since 2006.

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Figure3 – The residential energy consumption in mtoe per type of energy in France [152]. For domestic usage, solar collectors are till now mostly for individual hot water distri-bution but collective distridistri-bution is gaining ground gradually in France (ﬁgure 4). The relative slow down of the rate of installation from 2012 may be inferred to the recent ﬁscal policy less encouraging direct investment in renewable energy than in the past decade. In such a competitive context, a need has developed to predict, as accurate as possible, the performance of solar thermal devices. With that prediction, the best collector can be chosen at most economic way.

Figure4 – The rate of installed surface in m2 per year for each solar collector technology [152].

These solar thermal devices may contain either evacuated tubes or ﬂat-plate collectors. Still the use of evacuated tube solar collectors remains modest compared with glass col-lectors. This due to its recent development of the former technology where research is in perpetual dynamics (ﬁgure5).

Figure 5 – The installed surface in m2 per year for each collector technology [152].

2 Motivation and objectives

Despite the ubiquity of heat pipes and the large database that helps describing scienti-ﬁcally the phenomena occurring therein, there are still many areas in speciﬁc application

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and manufacturing considerations which require further attention to get a deeper unders-tanding of the involved phenomena and their impact on their functioning. The following work presents novel and additional eﬀort to the common knowledge of screen mesh wick heat pipes used in solar collectors. The main purposes of the research are:

1. To model and simulate capillary wicked heat pipe using Lattice Boltzmann Method. 2. To compare the performance of heat pipes under diﬀerent working conditions in order to sketch the device of best performance.

3. To study the performance of heat pipe used in solar collectors numerically, optimize computationally, and experimentally for diﬀerent working conditions and conﬁgurations.

3 Manuscript overview/outline

The thesis manuscript is organized as follows:

- Chapter one presents an introduction of heat pipes: working principal, construction, types, operating limits and their application. Focusing on heat pipes in solar collectors, a detailed literature review is presented and discussed.

- Chapter two outlines the theory behind the lattice Boltzmann method: background, dif-ferent approaches for Navier-stockes equation derivation, Boltzmann equation and boun-dary conditions implementation.

- Chapter three presents the detailed derivation of the axisymmetric lattice Boltzmann model and its validation. An enhanced derived model is then proposed.

- Chapter four describes the developed numerical model used to solve the proposed heat pipe configuration along with validations. Different test cases are studied to analyze the effect of various parameters (working fluid, porous medium, etc.).

- Chapter five presents the experimental setup built in this study, the design and construc-tion of the heat pipe used, including a detailed descripconstruc-tion of the setup and the protocol followed. Then, the experimental results are analyzed and discussed where different heat pipe configurations used in solar collectors are compared under different working condi-tions.

- Chapter six concludes the manuscript and recall its main ﬁndings, ties the result of the study to theory and practice, and suggestions for improvement in future work.

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Chapter 1 Generalities and state of the art

Abstract

This chapter presents a track of state of arts related to heat pipes: its working prin-cipal, types, limits and applications. A particular attention is given for heat pipes used in solar energy applications: their interest, design and applications. Finally, a literature review on heat pipes and their applications in solar collectors that would guide us throu-ghout this thesis is discussed.

Résumé

Ce chapitre présente une généralité sur l’état de l’art lié aux caloducs: leur principe de fonctionnement, types, limites et applications. Nous mettons l’accent sur les caloducs utilisés dans les applications solaires: leur intérêt, conceptions et applications. Enﬁn, nous développons avec minutie une revue de la littérature sur les caloducs et leur application dans les collecteurs solaires qui nous guiderait le long de ces travaux de thèse.

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1.1 Historical development and background of heat

pipes

The development of heat pipes traces back to Jacob Perkins in 1836, who was the first to publish a patent on the concept of the Perkins tube [214]. This tube is basically a form of wickless gravity-assisted thermosyphon. The design, as shown in figure 1.1, was a closed tube containing a small quantity of water operating in either a single or two-phase cycle to transfer heat from a furnace to a boiler. A heat source placed at the bottom of the tube coil causes boiling of water in the closed loop. The resulting vapor generated in the tube moves upward due to buoyancy. When coming in contact with cooler walls, the vapor condenses, and the liquid falls down the coil of the pipe back to the furnace, where it evaporates again. Because there is no wick structure in the system, it can operate only when the boiler is placed above the furnace. The thermosyphon concept remained unchanged for about 50 years. Therefore, the Perkins tube became an essential part of the history of the heat pipe. Through trial and error, Perkins found that the ideal volume of water in the tube was 32%. Any more than that resulted in the tube being completely filled with water and blocking the vapor flow. Any less than that resulted in complete vaporization, dry out, and overheating. In the development of the Perkins tube, the most interesting improvements were made by L. P. Perkins and W. E. Buck [69]. Their work focused on the study of the fluid inventory. While water was the only specific working fluid, they tested the use of anti-freeze type fluids, and fluids having higher boiling tem-perature at atmospheric pressure than water.

Figure 1.1 – Drawing of Perkin’s boiler [229].

It was in 1944 when the concept of the capillary-based heat pipes was ﬁrst put forward was suggested by R. S. Gaugler, who was working on refrigeration problems at that

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time, in General Motors. He patented a lightweight, heat transfer instrument which was supposedly applied to a refrigeration system [74]. His device consisted of a closed tube in which the liquid receives heat at one location causing the liquid to evaporate. The vapor travels down the length of the tube where it condenses and releases its latent heat. The liquid phase travels back up the tube by capillary pressure to start the process over. In order to move the liquid back up to a higher point, Gaugler suggested using a capillary structure consisting of a sintered iron wick to make the inner fluid return back to the evaporator, instead of gravity. However, it was not developed beyond the patent stage, as other technologies currently available at that time were applied to solve the particular thermal problem at General Motors Corporation. But throughout that period there was no great need for such a device, so the development made no serious impact for about twenty years. The 1960’s brought noticeable heat pipe developments. It was reinvented during 1963 when G. M. Grover and his co-workers, from Los Alamos Scientific Laboratory, designed a device and coined the name “heat pipe” (HP). In the words of Grover [86] “a heat pipe is a synergistic engineering structure which is equivalent to a material having thermal conductivity greatly exceeding that of any known metal”. In other words, a heat pipe is a passive two-phase heat transfer device able to transferring large quantities of heat with minimum temperature drop. He is often referred to as the inventor of a heat pipe. Later, he [85] built several prototypes of heat pipe, the first of which used water as working fluid and was soon followed by a sodium heat pipe which operated at higher temperature (1100 K) using wire mesh wick structures. Since that time, interest in the heat pipe concept developed rapidly both for space and terrestrial applications. In 1964, RCA was the first commercial organization to perform heat pipe research RCA® [127]. Work was carried out on many working fluids including metals, water, cesium, sodium, lithium, and bismuth using glass, copper, nickel, stainless steel, molybdenum and TZM molybdenum as heat pipe wall materials. At the same time the theory of the heat pipe became better understood; the most important contribution to this theoretical understanding was due to Cotter in 1965 [48]. Throughout 1969, NASA, which played an important role in heat pipe development in the 1960s particularly regarding applications and reliability in space flight, showed interest in using heat pipes to control spacecraft components temperature. Since heat pipes can operate in micro-gravitational fields due to capillary action without any external force field or pumping, most early efforts were directed toward space applications. The early development of terrestrial applications of heat pipes proceeded at a slow pace. However, due to the high cost of energy, especially in Japan and Europe, the industrial community began to appreciate the significance of heat pipes and thermosyphons in energy savings as well as design improvements in various applications. Through time, heat pipes progressed and modern applications of this technology range today from miniature heat pipes for cooling processors inside laptop computers, to groups of one centimeter diameter and two meters long pipes used in NASA spacecraft and pipes of five centimeter diameters (or more) which are used to cool injection molds used in plastic forming. The lengths of the pipes can vary from some centimeters to eight meters or even more.

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1.2 Heat pipe working principal

A heat pipe is a very simple device that transfers heat from one location to another, using the latent heat of vaporization. Heat pipes are referred to as the “superconductors” of heat owing to their important transfer capability with minimal heat loss over large dis-tances with minimal temperature drops, exceptional ﬂexibility, simple construction and easy control all without a need for external pumping power. Such a device consists of a closed container, a wick structure lined on the inner surface and a small amount of working ﬂuid in equilibrium with its own vapor.

Figure 1.2 – Heat pipe schematic description.

It has three main sections as shown in figure1.2; the evaporator, the adiabatic and the condenser sections. When heat is applied at the evaporator section of the heat pipe, the liquid temperature locally raises leading to the evaporation of the working fluid. Because of the saturation conditions this temperature difference results in a difference in vapor pressure, drives the vapor through the adiabatic section to the condenser, where the vapor condenses, releasing its latent heat of vaporization to the provided heat sink. The rate of vaporization is proportional to the heat absorbed in its latent form. The resulting condensate is pumped back to the evaporator of the container thanks to the capillary forces occurring along the menisci contained in the wick lining inside the pipe. The pumping can also be done by gravitation, in gravity-assisted heat pipes (thermosyphon). This process will continue as long as there is a sufficient capillary pressure to drive the condensate back to the evaporator. Therefore, as long as liquid is driven back to the evaporator, the heat pipe can continuously transport heat from the evaporator to the condenser section. Situations for which a heat pipe can no longer fulfill this transport are explained in section

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1.3 Heat pipe construction

In its conventional design, a heat pipe consists of a sealed tube that is partially filled with a working fluid. A wick, saturated with a working fluid, lines the inner side of the tube. In general, the performance of a heat pipe depends on several factors, such as its geometry, working fluid, capillary structure material, operating temperature, and applied heat flux and heat flux density. In the selection of a suitable combination of the above, inevitably a number of conflicting factors may arise. The chief bases for selection are discussed below.

1.3.1 Container materials

The issue of material compatibility and the results of life tests on heat pipes and ther-mosyphons remain critical aspects of heat pipe design and manufacturing. In particular, the generation of non-condensable gases that adversely affect the performance of heat pipes in either short or long term must be taken particularly seriously into account in the emerging technology of micro heat pipes and arrays of such devices. In fact, the heat pipe material must be chemically inert with the working fluid. Any chemical reaction will result in a by-product of non-condensible gas. A non-condensible gas is a gas, different from the working fluid vapor, that is not easily condensed by cooling. It consists mostly of nitrogen, light hydrocarbons, carbon dioxide, or other gaseous materials. So, the gases will collect in the condenser end of the heat pipe, swept thereby the following vapor, and obstruct a portion of the available heat dissipation area.

1.3.2 Working fluids

Since heat pipes utilize the phase change of the working ﬂuid to transport heat, the selection of the working ﬂuid is of paramount importance for enhancing their thermal performance.

A first consideration in the identification of a suitable working fluid is the operating vapor temperature range where a selection of fluids is shown in table 1.1. Within the approximate temperature range several possible working fluids may exist, and a variety of characteristics must be examined in order to determine the most acceptable among them for the considered application. Before starting heat pipe manufacturing, it is important to verify firstly if the desired working fluid is compatible or not with the suggested wick materials. Here we present some typical heat pipe working fluids and their compatibility with the wick material found in literature [229].

Hence, the prime requirements are: compatibility with wick and wall materials as many of the problems associated with long-life heat pipe operation are a direct consequence of material incompatibility; good thermal stability: the possibility of thermal degradation

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Working ﬂuid Boiling point at atmospheric pressure (◦_{C) Operation range (}◦_C) Helium -261 -271 to -269 Nitrogen -196 -203 to -160 Ammonia -33 -60 to 100 Pentane 28 -20 to 120 Acetone 57 0 to 120 Methanol 64 10 to 130 Ethanol 78 0 to 130 Water 100 30 to 200 Mercury 361 250 to 650 Potassium 774 500 to 1000 Sodium 1154 600 to 1200 Lithium 1340 1000 to 1800 Silver 2212 1800 to 2300

Table 1.1 – Heat pipe main working ﬂuids [229].

with certain organic fluids the fluid breaking down into different compounds; high thermal conductivity; low liquid and vapor viscosity; high surface tension: which enable the heat pipe to operate against gravity and to generate a high capillary driving force; wettability of wick and wall materials: the contact angle must be zero or very small with an acceptable freezing point [229]. All of the above criteria could be resumed through the figure of merit, Me, which is used as the thermal performance index of a certain working fluid for heat pipes. It is defined as:

Me= ρlhlvσ

µl

(1.1) The selection of the working ﬂuid must also be based on thermodynamic considerations which are concerned with the various limitations to heat ﬂow occurring within the heat pipe. These will be discussed in section 1.7.

The above mentioned requirements are not the only criteria for the selection of the working fluid. Other factors may, in a particular situation, be of greater importance. At slightly lower temperatures, 270-350 K, ammonia is a desirable fluid, although it requires care-ful handling to retain high purity. Acetone and alcohols are alternatives solutions having lower vapor pressures. These fluids are commonly used in heat pipes for space applica-tions. Water and methanol, both being compatible with copper, are often used in cooling electronic equipment.

The working fluids used in heat pipes have remained essentially the same, with the exception of the addition of nanoparticles. A great deal of research has been conducted on the use of nanofluids in wide range of heat pipe applications. Recently, Do et al. [54] mentioned that the formation of thin coating at the screen mesh wick of the evaporator is the principal reason for the enhancement of thermal performance of the heat pipes using nanofluids and it is not, as thought before, due to their equivalent thermophysical properties. Moreover, Yang et al. [304] and Kim et al. [142] indicated that the coating layer formed by nanoparticles improves the surface wettability by reducing the contact

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Working ﬂuid Recommended Not recommended

Ammonia Aluminum Copper

Carbon steel Nickel Stainless steel Acetone Copper Silica Aluminum Stainless steel

Methanol Copper Aluminum

Silica Stainless steel

Water Copper Aluminum

Monel Silica

347 Stainless steel Stainless steel Nickel Carbon steel Potassium, Sodium Stainless steel Titanium

Inconel

Table 1.2 – Working ﬂuids and their compatibility with heat pipe wick material.

angle and increasing the surface roughness, which in turn acts to increase the critical heat flux. Also, the coating layer induces liquid suction due to capillary wicking, which enhances the maximum heat flux [272]. Nevertheless, when life tests have to be higher than 10 years, some working fluids seem to lose their attractiveness. This may be dictated by health and safety considerations or by environmental pressures (for example in some countries in Europe the use of hydrofluorocarbons is being phased out in favor of fluids that contribute less to global warming).

1.3.3 Wick structure

As a ﬁrst approach, the thermal performance of a heat pipe can be characterized by both its overall thermal resistance and its maximum power in horizontal and vertical po-sitions. These characteristics depend mainly on the capillary structure, which is usually made of grooves, meshes, sintered powder or a combination of them as shown in ﬁgure1.3.

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Figure 1.3 – Diﬀerent wick structures used in heat pipes [229].

The wick structure inside the heat pipe works as a capillary pump, moving the liquid from the condenser to the evaporator through the adiabatic section. Besides the working fluid, the heat pipe geometry and material, it is one of the most important elements de-termining the performance of the heat pipe. To work effectively and efficiently, the wick structure must fulfill two requirements: sufficient capillary pressure and sufficient permea-bility. These two factors need special attention because the small pore structure creates large capillary pressure, whereas permeability requires large pores [53]. The capillary flow inside the wick structure is also determined by the contact angle between the liquid and the wick structure, known as the wettability, as stated by Shirazy et al. [258], where ca-pillarity occurs due to the attractive force between liquid molecules and solid molecules, forcing the liquid to flow through the porous media. The material of the wick structure may be metalic, composite, ceramic, etc. But it is difficult to obtain both high capillarity and high permeability from a single type wick structure with single pore properties (pore size or shape). Thus, it is necessary to investigate a “mixed” wick structure. Good com-promise between high capillary pressure and high permeability is found in some special wicks. One example is the biporous structure, which has two separate and distinct pore sizes in it. It includes two types of wicks: the first is made of large rough particles with small pores on the surface, and the second, which is called bidisperse wick structure, is made of clusters of small particles. A biomaterial such as coral is a material with a porous structure made of calcium carbonate deposits produced by stony corals from the animal realm. There are many types of coral, including branching, massive and tabulate corals. This biomaterial has relatively homogeneous pores, which are small in diameter. As a result of these small homogeneous pores, biomaterials have good capillarity. Biomaterials are also non-metallic with a tendency to oxidation significantly reduced.

It is worth to mention that the wick structure must be compatible with the chosen working ﬂuid. More details are given in Appendix 1.2.

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1.3.4 Charge filling

In the case of capillary pumped heat pipes, the liquid is supposed to fill in exactly the capillary structure. But, the volume of the liquid varies as a function of the average ope-rating temperature. A capillary structure saturated with liquid, without any liquid out of structure, is therefore not possible for all transferable powers with a given operating tem-perature. The consequences of this phenomenon are different depending on the operating conditions. For a heat pipe in horizontal position, it is possible to provide an optimum filling for the lowest operating temperature. Indeed, when the temperature increase, the fluid expands and an excess of liquid appears at the end of the condenser. This excess can only appear at the condenser since the porous medium is the only element liquid mixture outside the condensation zone. So the only consequence is a slight plug of liquid at the end of the condenser causing a very small decrease in performance. This can be compen-sated simply by a slight oversize of the length of the condenser. When the heat pipe is subjected to volume forces, the zone of accumulation of the liquid excess is a function of these volume forces. However, it can be noted that the effects are weak if the heat pipe capillary pumping forces are greater than the volumetric forces. Indeed, in this case the local differences in liquid filling of the capillary structure are small. Volume forces can also lead to angular dissymmetry in exchange coefficients when a radial component exists and is not completely balanced by the capillary forces. As a result, tests of heat pipes in terrestrial environment should be analyzed with particular attention.

1.4 The physics of heat pipes

At specific pressure conditions, two mechanisms occur. The first mechanism is that, at a certain specific temperature, the liquid vaporizes. The resulted vapor can only be condensed when the temperature reaches the saturation conditions. The second mecha-nism is that the amount of absorbed heat at the evaporator section is equal to the amount of heat rejected at the section of the condenser in steady state.

1.4.1 Fluid phases bulk flow

Since heat pipes need to work with the circulation of a fluid in a closed loop, knowing the main characteristics of the flows in the vapor and liquid phases represent a key element to understand their global behavior. Detailed studies have been carried out in order to define the most important parameters governing such flows. Due to its complexity, the details of mass and momentum equations are needed not only for vapor but also for the liquid in the porous medium. In addition, the equations of energy conservation with the phase change must be solved too. No analytical solution is available in general, numerical resolution remains the last resort although often being out of reach even for the present computers performance. Accordingly, the issue is to simplify as much as possible while

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keeping good model approximation of the actual mechanisms. The problem as a whole is usually addressed by artiﬁcially uncoupling the vapor and liquid domains.

Experimental validation is very diﬃcult because the measurements inside the heat pipes are extremely complex. The majority of the studies carried out are numerical and are subjected to quite restrictive conditions [110,235,319].

Vapor flow

The flow in the vapor phase can be separated into three distinct zones corresponding to the evaporator, the adiabatic and the condenser zone. On the evaporator, the vapor mass flow rate increases along the evaporator axis due to the introduction of vapor resulting from liquid vaporization while the opposite phenomenon occurs at the condenser. The adiabatic region is, ideally, only the location of pressure drops due to flow circulation. Vapor pressure variations are the result of two distinct mechanisms. Firstly, the friction causes pressure drop in the overall flow. Secondly, in the evaporation zone at the interface, the vapor has a mean velocity almost orthogonal to the axial flow. The longitudinal motion of the fluid flow must therefore be achieved by a pressure variation.

Liquid flow

Whether the flow in the liquid phase is subjected to the same stresses as the vapor phase along their common interface, the consequences are very different. The large ratio of the liquid-vapor densities results in a reversal of the relative importance of the variations in inertial pressure and the effect of the volume forces. Indeed, since the velocity of the liquid flow is very low, the inertial pressure variations are totally negligible, whereas the effect of the forces of volume becomes dominant. Friction plays an important role in the fluid circulation, in particular, for heat pipes with capillary pumping.

1.4.2 Liquid/vapor interface

Description of the liquid/vapor interface

While the structure of solids surfaces and insoluble ﬁlms is fairly well established [45], the structure of liquid surfaces in contact with its own saturated vapor remains somewhat obscure until now due to the complexity of the phenomena involved [156]. During the last decades, many research works were focused on the understanding of the transfer pro-cesses occurring in liquid/vapor interface [21,222,295]. The microscopic theories provide a description based on the ﬁrst principle. They are dealing, however, with complicated mathematical formalisms and it is not possible until now to translate their exact results into useful macroscopic language [295]. In contrast, the methods of nonequilibrium

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ther-modynamics and hydrodynamics are easier to handle and seem to be more appropriate to describe the problem [18]. The Gibbs theory of surface tension assumes uniform pro-prieties of the liquid up to the vapor phase on the other hand the theory of van der Waals involves the assumption of a continuous transition from liquid to vapor. Neither of the theories allows for an evaluation of the thickness of the transitional region except by the introduction of an arbitrary potential function. The conﬂict between the theory of van der Waals, which maintains the presence of a non-uniform capillary layer, and the experimental evidence may be more apparent than real.

The capillarity and surface tension

Molecules in a liquid appeal each other. A molecule in a liquid is attracted by the surrounding molecules and, on average, a molecule in the bulk of the ﬂuid experiences no net force. In the case of a molecule at or near the surface of a liquid, the forces of attraction will no longer balance out and the molecule will experience a resultant inward force. Because of this eﬀect the liquid will tend to take up a shape having minimum surface area; in the case of a free falling drop in a vacuum this would be a sphere. Due to this spontaneous tendency to contract, the liquid surface behaves rather like a rubber membrane under tension. In order to increase the surface area work must be done on the liquid. The energy associated with this work is known as the free surface energy, and the corresponding free surface energy per unit surface area is called surface tension and is given the symbol σl. Hence, the Laplace-Young equation could be introduced by:

∆p = σ

R (1.2)

where ∆p is the Laplace pressure and R is the principal radius of curvature.

The surface tension is numerically equal to the surface energy per unit area measured in any consistent set of units, e.g. N/m. Since latent heat of vaporisation, L, is a measure of the forces of attraction between the molecules of a liquid, we might expect surface energy or surface tension σl to be related to L. This is found to be the case. Solids also will have a free surface energy, which magnitude is found to be similar to the value for the same material in the molten state. When a liquid is in contact with a solid surface, molecules in the liquid adjacent to the solid will experience forces from the molecules of the solid in addition to the forces from other liquid molecules. Depending on whether these solid/liquid forces are attractive or repulsive the liquid-solid surface will curve inward or outward. The two best-known examples of attractive and repulsive forces are water and mercury, respectively on copper. Where the forces are attractive the liquid is said to ’wet’ the solid. The angle of contact made by the liquid surface with the solid is known as the contact angle, θ. For wetting liquids, θ lies between 0◦_{and 90}◦_{and for non-wetting liquids,}

θ > 90◦_{. The condition for wetting to occur is that the total surface energy is reduced by}

wetting:

σsl+ σlv < σsv (1.3)

where the subscripts, s, l and v refer to solid, liquid and vapor phases, respectively. Wetting will not occur if σsl + σlv > σsv while the intermediate condition of partial

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wetting is σsl+ σlv = σsv.

1.5 Heat pipe applications

Since the ﬁrst basic heat pipe concept was proposed by Gaugler (1944), heat pipes have been widely applied to a variety of both simple and complex designs for space and terrestrial applications.

1.5.1 Terrestrial applications

Currently the greatest use of heat pipes is in the cooling of computers and electronic components [183]. The utilization of heat pipes and vapor chamber to spread and transfer heat was a key factor for extending the air cooling limit capability for high performance computers. The main thermal solutions based on heat pipes are the vapor chamber, mi-niature and micro heat pipes with micro axial grooves, remote heat exchangers and hybrid systems. Because of its small dimensions, some diﬃculties, in manufacturing, degassing and charging, are expected.

Recently, researches have been reported where developments of high interest in heat pipe technology for heat recovery were made [181,257]. Studies have analyzed the ap-plication of heat pipes on the thermal performance of heat recovery systems. In air-air conditioning facilities consisting of two CHPs and indirect evaporative systems, ap-plying the mixed-energy recovery system makes possible a recovery form the return air-flow. This improves significantly the energy efficiency and reduces the environmental im-pact [59,173,202,305].

The demand for using heat pipes in renewable energy systems along with building heat recovery, highlighting novel concepts and requirements, is increasing. Several terrestrial applications make use of heat pipes in heat exchangers for higher heat transfer rates. Consequently, heat pipes have been expansively used in various energy storage systems due to their passive operation and suitability for heat delivery [31]. The unique method of operation of heat pipes including phase-change materials (PCMs) provide a better effi-ciency pattern over conventional heat exchangers in major operation conditions including temperature stratification in hot water storage tanks. However, in the case where the working fluid passes through the PCM storage tank, extending the piping length inside the tank causes a large pressure drop of the working fluid and a large decrease in the effective PCM storage volume for conventional latent heat thermal energy storage. Inte-grating HPs into the system can overcome this problem. Other widespread commercial use of heat pipes is integrating them into solar collectors in order to transfer both the direct and diffuse solar radiation to the water stream. One of the most common uses for heat pipes associated with storage is to absorb solar energy and transfer it to water, either

Numerical and Experimental Study of Heat Pipes Used in Solar Applications

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DOCTEUR DE L’ÉCOLE NATIONALE SUPÉRIEURE

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Numerical and experimental study of heat pipes used in

solar applications

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Table of contents

List of figures

List of tables

Nomenclature

1

Context

2

Motivation and objectives

3

Manuscript overview/outline

Chapter 1

Generalities and state of the art

Abstract

Résumé

1.1

Historical development and background of heat

pipes

1.2

Heat pipe working principal

1.3

Heat pipe construction

1.3.1

Container materials

1.3.2

Working fluids

1.3.3

Wick structure

1.3.4

Charge filling

1.4

The physics of heat pipes

1.4.1

Fluid phases bulk flow

1.4.2

Liquid/vapor interface

1.5

Heat pipe applications

1.5.1

Terrestrial applications